Problem: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 6x + 9$ and $ BC = 4x + 23$ Find $AC$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {6x + 9} = {4x + 23}$ Solve for $x$ $ 2x = 14$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 6({7}) + 9$ $ BC = 4({7}) + 23$ $ AB = 42 + 9$ $ BC = 28 + 23$ $ AB = 51$ $ BC = 51$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {51} + {51}$ $ AC = 102$